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<p>For <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, B. Simon[<CitationRef CitationID="CR16">16</CitationRef>] studied the unboundedness of the Weyl transform for symbol belonging to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^p({\mathbb {R}^n\times \mathbb {R}^n})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this article, we study the analog of unboundedness of the Weyl transform on some nonunimodular groups, namely, the affine group, similitude group, and affine Poincaré group.</p>

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Weyl transform on some Nonunimodular Groups

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Santosh Kumar Nayak

摘要

For \(p>2\) p > 2 , B. Simon[16] studied the unboundedness of the Weyl transform for symbol belonging to \(L^p({\mathbb {R}^n\times \mathbb {R}^n})\) L p ( R n × R n ) . In this article, we study the analog of unboundedness of the Weyl transform on some nonunimodular groups, namely, the affine group, similitude group, and affine Poincaré group.